题意：
给出一个字符串str，问前缀与后缀匹配的串在str中出现了几次。
思路：
前缀与后缀匹配就是next数组的意义，根据next数组可以从后往前统计出子串在母串中出现的次数。
代码：
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <cstring>
#include <cctype>
#include <cstdlib>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <map>
#include <list>
#include <set>
#include <stack>
#include <queue>
#include <string>
#include <sstream>
#define pb push_back
#define X first
#define Y second
#define ALL(x) x.begin(),x.end()
#define INS(x) inserter(x,x.begin())
#define pii pair<int,int>
#define qclear(a) while(!a.empty())a.pop();
#define lowbit(x) (x&-x)
#define sd(n) scanf("%d",&n)
#define sdd(n,m) scanf("%d%d",&n,&m)
#define sddd(n,m,k) scanf("%d%d%d",&n,&m,&k)
#define mst(a,b) memset(a,b,sizeof(a))
#define cout3(x,y,z) cout<<x<<" "<<y<<" "<<z<<endl
#define cout2(x,y) cout<<x<<" "<<y<<endl
#define cout1(x) cout<<x<<endl
#define IOS std::ios::sync_with_stdio(false)
#define SRAND srand((unsigned int)(time(0)))
typedef long long ll;
typedef unsigned long long ull;
typedef unsigned int uint;
using namespace std;
const double PI=acos(-1.0);
const int INF=0x3f3f3f3f;
const ll INFF=0x3f3f3f3f3f3f3f3f;
const ll mod=998244353;
const double eps=1e-8;
const int maxn=100005;
const int maxm=10005;
void getnext(char* p,int* f){
int m=strlen(p);
f[0]=0;
f[1]=0;
for(int i=1;i<m;i++){
int j=f[i];
while(j&&p[i]!=p[j])j=f[j];
f[i+1]=p[i]==p[j]?j+1:0;
}
}
char str[maxn];
int nxt[maxn];
int ans[maxn];
void solve() {
scanf("%s",str);
getnext(str,nxt);
int len=strlen(str);
for(int i=0;i<=len;i++){
ans[i]=1;
}
for(int i=len;i;i--){
ans[nxt[i]]+=ans[i];
}
vector<pii>v;
for(int i=len;i;i=nxt[i]){
v.pb(make_pair(i,ans[i]));
}
sort(ALL(v));
printf("%d\n",v.size());
for(int i=0;i<v.size();i++){
printf("%d %d\n",v[i].X,v[i].Y);
}
return ;
}
int main() {
#ifdef LOCAL
freopen("in.txt","r",stdin);
// freopen("out.txt","w",stdout);
#else
// freopen("","r",stdin);
// freopen("","w",stdout);
#endif
solve();
return 0;
}